19 research outputs found
Inequality in resource allocation and population dynamics models
The Hassell model has been widely used as a general discrete-time population
dynamics model that describes both contest and scramble intraspecific
competition through a tunable exponent. Since the two types of competition
generally lead to different degrees of inequality in the resource distribution
among individuals, the exponent is expected to be related to this inequality.
However, among various first-principles derivations of this model, none is
consistent with this expectation. This paper explores whether a Hassell model
with an exponent related to inequality in resource allocation can be derived
from first principles. Indeed, such a Hassell model can be derived by assuming
random competition for resources among the individuals wherein each individual
can obtain only a fixed amount of resources at a time. Changing the size of the
resource unit alters the degree of inequality, and the exponent changes
accordingly. The Beverton-Holt and Ricker models can be regarded as special
cases of the derived Hassell model. Two additional Hassell models are derived
under some modified assumptions.Comment: 13 pages, 5 figure
Geometrical Construction of Heterogeneous Loop Amplitudes in 2D Gravity
We study a disk amplitude which has a complicated heterogeneous matter
configuration on the boundary in a system of the (3,4) conformal matter coupled
to two-dimensional gravity. It is analyzed using the two-matrix chain model in
the large N limit. We show that the disk amplitude calculated by
Schwinger-Dyson equations can completely be reproduced through purely
geometrical consideration. From this result, we speculate that all
heterogeneous loop amplitudes can be derived from the geometrical consideration
and the consistency among relevant amplitudes.Comment: 13 pages, 11 figure
Splitting of Heterogeneous Boundaries in a System of the Tricritical Ising Model Coupled to 2-Dim Gravity
We study disk amplitudes whose boundaries have heterogeneous matter states in
a system of conformal matter coupled to 2-dim gravity. They are
analysed by using the 3-matrix chain model in the large limit. Each of the
boundaries is composed of two or three parts with distinct matter states. From
the obtained amplitudes, it turns out that each heterogeneous boundary loop
splits into several loops and we can observe properties in the splitting
phenomena that are common to each of them. We also discuss the relation to
boundary operators.Comment: 10 pages, Latex, 3 figure
Boundary operators and touching of loops in 2d gravity
We investigate the correlators in unitary minimal conformal models coupled to
two-dimensional gravity from the two-matrix model. We show that simple fusion
rules for all of the scaling operators exist. We demonstrate the role played by
the boundary operators and discuss its connection to how loops touch each
other.Comment: 19 pages, Latex, 3 Postscript figure
Interaction of boundaries with heterogeneous matter states in matrix models
We study disk amplitudes whose boundary conditions on matter configurations
are not restricted to homogeneous ones. They are examined in the two-matrix
model as well as in the three-matrix model for the case of the tricritical
Ising model. Comparing these amplitudes, we demonstrate relations between
degrees of freedom of matter states in the two models. We also show that they
have a simple geometrical interpretation in terms of interactions of the
boundaries. It plays an important role that two parts of a boundary with
different matter states stick each other. We also find two closed sets of
Schwinger-Dyson equations which determine disk amplitudes in the three-matrix
model.Comment: 20 pages, LaTex, 2 eps figures, comments added, introduction
replaced, version to appear in Nuclear Physics